Excited states of a phosphorus pair in silicon: Combining valley-orbital interaction and electron-electron interactions

Excitations of impurity complexes in semiconductors cannot only provide a route to fill the terahertz gap in optical technologies but can also play a role in connecting local quantum bits efficiently to scale up solid-state quantum-computing devices. However, taking into account both the interactions among electrons/holes bound at the impurities and the host band structures is challenging. Here we combine first-principles band-structure calculations with quantum-chemistry methodology to evaluate the ground and excited states of a pair of phosphorous (shallow donors) impurities in silicon within a single framework. We account for the electron-electron interaction within a broken-symmetry Hartree-Fock approach, followed by a time-dependent Hartree-Fock method to compute the excited states. We adopt a Hamiltonian for each conduction-band valley including an anisotropic kinetic energy term, which splits the 2 p 0 and 2 p ± transitions of isolated donors by ∼ 4 meV, in good agreement with experiments. Our single-valley calculations show the optical response is a strong function of the optical polarization and suggest the use of valley polarization to control optics and reduce oscillations in exchange interactions. When taking into account all valleys, we have included valley-orbital interactions that split the energy levels further. We find a gap opens between the 1 s → 2 p transition and the low-energy charge-transfer states within 1 s manifolds (which become optically allowed because of interdonor interactions). In contrast to the single-valley case, we also find charge-transfer excited states in the triplet sector, thanks to the extra valley degrees of freedom. Our computed charge-transfer excited states have a qualitatively correct energy as compared with previous experimental findings; additionally, we predict a set of excitations below 20 meV. Calculations based on a statistical average of nearest-neighbor pairs at different separations suggest that THz radiation could be used to excite the donor pairs spin-selectively. Our approach can readily be extended to other types of donors such as arsenic, and more widely to other semiconducting host materials such as germanium, zinc oxides, and gallium nitride, etc